Proposition 17 
[1]}
Let \(\nu \)  be an \(L\) -layer stochastic neural network satisfying (a)-(c) in section REF  such that \(t^{(L)}=-\infty \)  and \(p=n_L=1\) , that is, \(\nu :\mathbb {R}^d \rightarrow \mathbb {R}\) . Let the score function \(s: \mathbb {R} \rightarrow \mathbb {R}\)  be injective with decision threshold \(c\)  in its range. If \(\nu =f \oslash g\) , where \(f\)  and \(g\)  are tropical polynomials, then the number of connected positive regions is at most \(\mathcal {N}(f)\) , while the number of connected negative regions is at most \(\mathcal {N}(g)\) .

